Q5 of 145 Page 417

If the mean and mode of a frequency distribution be 53.4 and 55.2 respectively, find the median.

Given: mean = 53.4 and mode = 55.2

We have to find the median.


By empirical formula,


Mode = 3(Median) – 2(Mean)


⇒ 3(Median) = Mode + 2(Mean)


⇒ Median = [Mode + 2(Mean)]/3


⇒ Median = [55.2 + 2(53.4)]/3


⇒ Median = [55.2 + 106.8]/3


⇒ Median = 162/3 = 54


∴ Median = 54


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3

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10 - 15



15 - 20



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 4

Consider the following frequency distribution:



















Class interval



0 - 5



6 - 11



12 - 17



18 - 23



24 - 29



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13



10



15



8



11



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 6

In the table given below, the times taken by 120 athletes to run a 100 - m - hurdle race are given.





















Class



13.8 - 14



14 - 14.2



14.2 - 14.4



14.4 - 14.6



14.6 - 14.8



14.8 - 15



Frequency



2



4



15



54



25



20



Find the number of athletes who completed the race in less than 14.6 seconds.

 7

Consider the following frequency distribution:



















Class



0 - 5



6 - 11



12 - 17



18 - 23



24 - 29



Frequency



13



10



15



8



11



Find the upper limit of the median class.